Estimating Probability of Life on Mars.

Methodology

We are going to apply the theory
of based on observations hypotheses reevaluation, to the no-life on Mars
hypothesis. We have to start from the higher margin of a priory probability
of the no-life hypothesis, relative to the life hypothesis, for
example R=100000.

Then the theory allows us to calculate the R after
series of observations ABCDE…,

R|ABCDE… = R *
K(A) * K(B) * K(C) * K(D) * K(E) * …

where
K(X)=P(X|H)/P(X|~H)

If we have enough observations, the initial bias of the
hypothesis relative probability estimate does not really matter /if it is not
zero/, since the corrections will eventually overcome it.

Conditional probabilities of observed facts A, B, …must be estimated from the available data.
More precisely, we need centered or lower bound estimate under the life
condition, and upper bound estimate under the no life condition.

Estimating hypothesis probability correction coefficients.

The objects of interest are those that appear, compared to
others, the most likely to be of the biological origin. Such objects with
practical certainty are of the biological origin, on the condition that life
hypothesis is correct.

A target object is being presented as a base and a number of
features. The base’s probability is being estimated from its relative observed
frequency in the imagery.

The features’ probabilities are being estimated as
conditioned on the base’s presence - using applicable physical considerations,
and/or relative observed feature frequency in the imagery.

Under the no-life hypothesis features b, c,
d … are independent:

P(b, c, d
...)=p(b)*p(c)*p(d)…

Under the life hypothesis there is a relatively high
conditional probability

P(b, c,
d...)=p(a)*P(c, d...|b)

We consider the K(~H|A) , with H beingthe
life hypothesis and b the base feature:

K(~H|A)=(
p(c)*p(d)*…) / P(c, d...|b)

To measure with sufficient precision the probabilities
involved, we can count the pertinent objects, observed in the imagery.

Estimating particular
observations.

Basic estimates:

Total relevant images 10,000

Image area size 10x10 m

Relevant objects in the area 10

Total covered area 1,000,000 m2

Total objects 100,000

Average object area 10 m2

Unique feature probability 1/10,000

Martian

K(~H|A) is estimated as probability of having a
white, egg shape rock, ofsize larger
than base_size/10, on top of the black base rock.

Egg shape white rocks probability< 1/100.

Egg shape white rocks count< 1000.

Getting on top of base rock< 1000 * 1/1,000,000 * 1/10=1/10,000

Suit feature probability~1/10,000< 1/1000

K(~H|A)=1/10,000,000

Hooked
creature

Hook feature probability~1/10,000

K(~H|A)=1/10,000

The axe

K(~H|A)<1/10,000

The flowers

K(~H|A)<1/10,000

Berries on
stalk

Bent stalk feature probability<1/1000

Berry on a bent stalk << 1/1,000,000

Double 10^-18

K(~H|A)<10^-18

A girl

K(~H|A)<1/10000

A girl head portrait

K(~H|A)<10^-8

Coin

K(~H|A)<1/10000

The tree fossil

More than two unique features, prominently the blade

K(~H|A)<< 10^-8

“Shell” on top

K(~H|A)< 10^-4

“Cube”

K(~H|A)< 10^-4

Horn

K(~H|A)< 10^-4

***

The current total no-life hypothesis probability reduction
coefficient: